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Optimal spending of a wealth fund in the discrete time life cycle model

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  • Aase, Knut K.

    (Dept. of Business and Management Science, Norwegian School of Economics)

Abstract

The paper analyses optimal spending of an endowment fund. We use the life cycle model for both expected utility and recursive utility in discrete time. First we find the optimal consumption and investment policies for both kinds of utility functions. This we apply to a sovereign wealth fund that invests broadly in the international financial markets. We demonstrate that the optimal spending rate, i.e., the consumption to wealth ratio, is significantly lower than the fund’s expected real rate of return. Using the expected return as the spending rate, implies that the fund’s value converges towards 0 with probability 1 and also in expectation, as time goes. For both kinds of long term convergence we find closed form threshold values. Spending below these values secures that the fund will last ”forever”. For reasonable values of the preference parameters, the optimal spending rate is demonstrated to satisfy these long term requirements.

Suggested Citation

  • Aase, Knut K., 2023. "Optimal spending of a wealth fund in the discrete time life cycle model," Discussion Papers 2023/7, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2023_007
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    File URL: https://hdl.handle.net/11250/3070742
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    References listed on IDEAS

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    1. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    2. Campbell, John Y. & Sigalov, Roman, 2022. "Portfolio choice with sustainable spending: A model of reaching for yield," Journal of Financial Economics, Elsevier, vol. 143(1), pages 188-206.
    3. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    4. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
    5. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
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    More about this item

    Keywords

    Life cycle model; optimal spending rate; endowment funds; expected utility; recursive utility; risk aversion; EIS; consumption to wealth ratio; almost sure convergence; 1st mean convergence;
    All these keywords.

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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